Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 16 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.9680962443200812275617.1	x^20 - x^19 + 7x^18 - 8x^17 + 19x^16 - 11x^15 + 8x^14 + 16x^13 - 16x^12 + 21x^11 + 7x^10 - 14x^9 + 38x^8 - 35x^7 + 32x^6 - 7x^5 - 4x^4 + 8x^3 - 3x^2 + 1	\( 7^{10}\cdot 17^{11} \)	20T144	Trivial
20.4.46484025093233137504237.1	x^20 - 3x^19 + 3x^18 + 8x^17 - 29x^16 + 42x^15 - 30x^14 - 3x^13 + 4x^12 + 33x^11 - 18x^10 - 83x^9 + 164x^8 - 175x^7 + 134x^6 - 65x^5 + 22x^4 - 2x^3 - 5x^2 + 2x - 1	\( 11^{10}\cdot 13^{11} \)	20T144	Trivial
20.4.474367159716839801505233.1	x^20 - x^19 - 4x^18 + 9x^17 - 8x^16 - 2x^15 + 35x^14 - 86x^13 + 77x^12 + 61x^11 - 257x^10 + 356x^9 - 235x^8 - 115x^7 + 512x^6 - 677x^5 + 532x^4 - 266x^3 + 82x^2 - 14x + 1	\( 7^{12}\cdot 17^{11} \)	20T144	Trivial
20.0.2797798146085034747653313.1	x^20 - 6x^19 + 18x^18 - 42x^17 + 83x^16 - 131x^15 + 186x^14 - 262x^13 + 309x^12 - 303x^11 + 305x^10 - 229x^9 + 60x^8 - 80x^7 + 279x^6 - 429x^5 + 561x^4 - 547x^3 + 285x^2 - 70x + 13	\( 7^{10}\cdot 17^{13} \)	20T144	Trivial
20.16.3410541143285770263976611328125.1	x^20 - 6x^19 - 8x^18 + 90x^17 - 4x^16 - 531x^15 + 278x^14 + 1492x^13 - 1843x^12 - 1533x^11 + 6985x^10 - 2465x^9 - 13628x^8 + 10557x^7 + 10965x^6 - 12858x^5 - 756x^4 + 4520x^3 - 1110x^2 - 270x + 95	\( 3^{8}\cdot 5^{11}\cdot 239^{8} \)	20T144	Trivial (GRH)
20.12.30694870289571932375789501953125.1	x^20 - 5x^19 + 5x^18 + 15x^17 - 90x^16 + 309x^15 - 605x^14 + 550x^13 + 317x^12 - 1406x^11 + 1138x^10 + 155x^9 - 490x^8 + 89x^7 - 212x^6 + 368x^5 - 94x^4 - 86x^3 + 43x^2 - 2x - 1	\( 3^{10}\cdot 5^{11}\cdot 239^{8} \)	20T144	Trivial (GRH)
20.4.30694870289571932375789501953125.1	x^20 - 5x^19 + 25x^18 - 80x^17 + 227x^16 - 450x^15 + 779x^14 - 755x^13 - 7x^12 + 2527x^11 - 5899x^10 + 9385x^9 - 5714x^8 - 8718x^7 + 11721x^6 - 416x^5 - 2025x^4 + 1207x^3 - 1297x^2 - 228x + 361	\( 3^{10}\cdot 5^{11}\cdot 239^{8} \)	20T144	Trivial (GRH)
20.4.30694870289571932375789501953125.2	x^20 - 5x^19 + 23x^18 - 54x^17 + 71x^16 + 122x^15 - 907x^14 + 2565x^13 - 4229x^12 + 2381x^11 + 4295x^10 - 13113x^9 + 10976x^8 + 17838x^7 - 47694x^6 + 7092x^5 + 22104x^4 - 5130x^3 - 2916x^2 - 1134x - 81	\( 3^{10}\cdot 5^{11}\cdot 239^{8} \)	20T144	$[2]$ (GRH)
20.8.85263528582144256599415283203125.1	x^20 - 4x^19 - 9x^18 + 60x^17 + 26x^16 - 321x^15 - 223x^14 + 614x^13 + 1982x^12 + 681x^11 - 9262x^10 - 14732x^9 + 5610x^8 + 57138x^7 + 81093x^6 - 47073x^5 - 187816x^4 - 68040x^3 + 93770x^2 + 48025x - 995	\( 3^{8}\cdot 5^{13}\cdot 239^{8} \)	20T144	$[2]$ (GRH)
20.8.85263528582144256599415283203125.2	x^20 - 23x^18 - 15x^17 + 162x^16 + 259x^15 - 178x^14 - 867x^13 - 1054x^12 + 696x^11 + 2098x^10 - 5646x^9 - 12475x^8 + 4624x^7 + 15907x^6 - 7283x^5 - 9771x^4 + 14470x^3 + 12325x^2 - 310x - 1045	\( 3^{8}\cdot 5^{13}\cdot 239^{8} \)	20T144	$[2]$ (GRH)
20.16.276253832606147391382105517578125.1	x^20 - 35x^18 + 485x^16 - 3490x^14 + 14002x^12 - 30045x^10 + 25020x^8 + 18405x^6 - 43974x^4 + 11475x^2 + 10125	\( 3^{12}\cdot 5^{11}\cdot 239^{8} \)	20T144	Trivial (GRH)
20.12.767371757239298309394737548828125.1	x^20 - 10x^19 + 38x^18 - 39x^17 - 264x^16 + 1265x^15 - 2152x^14 - 596x^13 + 11186x^12 - 22584x^11 + 9350x^10 + 39944x^9 - 77472x^8 + 44190x^7 + 31876x^6 - 105543x^5 + 102557x^4 + 15219x^3 - 70483x^2 + 28531x - 1919	\( 3^{10}\cdot 5^{13}\cdot 239^{8} \)	20T144	Trivial (GRH)
20.0.3576211589862019840319539200000000000.1	x^20 + 31x^18 + 389x^16 + 2577x^14 + 9803x^12 + 21686x^10 + 26641x^8 + 15837x^6 + 3166x^4 + 235x^2 + 5	\( 2^{20}\cdot 3^{8}\cdot 5^{11}\cdot 239^{8} \)	20T144	$[818]$ (GRH)
20.20.3576211589862019840319539200000000000.1	x^20 - 31x^18 + 389x^16 - 2577x^14 + 9803x^12 - 21686x^10 + 26641x^8 - 15837x^6 + 3166x^4 - 235x^2 + 5	\( 2^{20}\cdot 3^{8}\cdot 5^{11}\cdot 239^{8} \)	20T144	Trivial (GRH)
20.0.32185904308758178562875852800000000000.1	x^20 + 35x^18 + 455x^16 + 2940x^14 + 10402x^12 + 20795x^10 + 23450x^8 + 14595x^6 + 4806x^4 + 765x^2 + 45	\( 2^{20}\cdot 3^{10}\cdot 5^{11}\cdot 239^{8} \)	20T144	$[2, 1730]$ (GRH)
20.20.32185904308758178562875852800000000000.1	x^20 - 45x^18 + 693x^16 - 5090x^14 + 20514x^12 - 48945x^10 + 71522x^8 - 64065x^6 + 33966x^4 - 9675x^2 + 1125	\( 2^{20}\cdot 3^{10}\cdot 5^{11}\cdot 239^{8} \)	20T144	Trivial (GRH)